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A075192 Numbers k such that k^4 is an interprime = average of two successive primes.

%I A075192 #19 May 25 2021 02:55:52
%S A075192 3,5,8,21,55,66,87,99,104,105,110,120,129,135,141,144,152,168,172,186,
%T A075192 187,192,211,222,243,279,283,295,297,321,342,385,395,398,408,425,426,
%U A075192 460,520,541,559,597,626,627,638,642,657,666,673,680,713,755,759,765
%N A075192 Numbers k such that k^4 is an interprime = average of two successive primes.
%C A075192 Interprimes are in A024675, even interprimes are in A072568, odd interprimes are in A072569 n^2 as interprimes are in A075190, n^3 as interprimes are in A075191, n^5 as interprimes are in A075228, n^6 as interprimes are in A075229, n^7 as interprimes are in A075230, n^8 as interprimes are in A075231, n^9 as interprimes are in A075232, n^10 as interprimes are in A075233, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.
%H A075192 Amiram Eldar, <a href="/A075192/b075192.txt">Table of n, a(n) for n = 1..10000</a>
%e A075192 3 belongs to this sequence because 3^4 = 81 is the average of two successive primes 79 and 83.
%p A075192 s := 4: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%t A075192 intprQ[n_]:=Module[{c=n^4},c==Mean[{NextPrime[c],NextPrime[c,-1]}]]; Select[Range[800],intprQ] (* _Harvey P. Dale_, Dec 01 2013 *)
%Y A075192 Cf. A024675, A072568, A072569, A075190, A075191.
%Y A075192 Cf. A075228, A075229, A075230, A075231, A075232, A075233, A075234.
%K A075192 nonn
%O A075192 1,1
%A A075192 _Zak Seidov_, Sep 09 2002
%E A075192 Edited by _Robert G. Wilson v_ Sep 14 2002